geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, the pseudo great rhombicuboctahedron is one of the two pseudo uniform polyhedra, the other being the convex

elongated square gyrobicupola In geometry, the elongated square gyrobicupola or pseudo-rhombicuboctahedron is one of the Johnson solids (). It is not usually considered to be an Archimedean solid, even though its Face (geometry), faces consist of regular polygons that meet ...

or pseudo rhombicuboctahedron. It has the same vertex figure as the

nonconvex great rhombicuboctahedron In geometry, the nonconvex great rhombicuboctahedron is a nonconvex uniform polyhedron, indexed as U17. It has 26 faces (8 triangles and 18 squares), 48 edges, and 24 vertices. It is represented by the Schläfli symbol rr and Coxeter-Dynkin dia ...

(a uniform polyhedron), but is not a uniform polyhedron (due to not being isogonal), and has a smaller symmetry group. It can be obtained from the great rhombicuboctahedron by taking a square face and the 8 faces with a common vertex to it (forming a

crossed square cupola In geometry, the crossed square cupola is one of the nonconvex Johnson solid isomorphs, being topologically identical to the convex square cupola. It can be obtained as a slice of the nonconvex great rhombicuboctahedron or quasirhombicuboctahedr ...

) and rotating them by an angle of . It is related to the

in the same way that the pseudo rhombicuboctahedron is related to the rhombicuboctahedron.

Related polyhedra

The pseudo-great rhombicuboctahedron may also be termed an ''elongated crossed square gyrobicupola'', in analogy to the name of the ''elongated square gyrobicupola''.

References

*. Reprinted in .

External links

George Hart - Pseudo Rhombicuboctahedra
* {{KlitzingPolytopes, ../incmats/gyquerco.htm, , gyquerco Pseudo-uniform polyhedra